%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU297+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:52:46 PM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 18
% Syntax : Number of formulae : 144 ( 23 unt; 16 def)
% Number of atoms : 550 ( 56 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 635 ( 229 ~; 292 |; 82 &)
% ( 22 <=>; 8 =>; 0 <=; 2 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 16 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 206 ( 0 sgn 159 !; 47 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2] :
( ( element(X1,powerset(powerset(X0)))
& relation(X2)
& function(X2) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,powerset(relation_dom(X2)))
& in(relation_image(X2,X4),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_xboole_0__e6_27__finset_1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( ( element(X1,powerset(powerset(X0)))
& relation(X2)
& function(X2) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,powerset(relation_dom(X2)))
& in(relation_image(X2,X4),X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f38,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(powerset(X0)))
& relation(X2)
& function(X2) )
=> ( ! [X3,X4,X5] :
( ( X3 = X4
& in(relation_image(X2,X4),X1)
& X3 = X5
& in(relation_image(X2,X5),X1) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,powerset(relation_dom(X2)))
& X5 = X4
& in(relation_image(X2,X4),X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',s1_tarski__e6_27__finset_1__1) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( element(X1,powerset(powerset(X0)))
& relation(X2)
& function(X2) )
=> ( ! [X3,X4,X5] :
( ( X3 = X4
& in(relation_image(X2,X4),X1)
& X3 = X5
& in(relation_image(X2,X5),X1) )
=> X4 = X5 )
=> ? [X6] :
! [X7] :
( in(X7,X6)
<=> ? [X8] :
( in(X8,powerset(relation_dom(X2)))
& X7 = X8
& in(relation_image(X2,X7),X1) ) ) ) ),
inference(rectify,[],[f38]) ).
fof(f47,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( in(X4,X3)
<~> ( in(X4,powerset(relation_dom(X2)))
& in(relation_image(X2,X4),X1) ) )
& element(X1,powerset(powerset(X0)))
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f48,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( in(X4,X3)
<~> ( in(X4,powerset(relation_dom(X2)))
& in(relation_image(X2,X4),X1) ) )
& element(X1,powerset(powerset(X0)))
& relation(X2)
& function(X2) ),
inference(flattening,[],[f47]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ? [X6] :
! [X7] :
( in(X7,X6)
<=> ? [X8] :
( in(X8,powerset(relation_dom(X2)))
& X7 = X8
& in(relation_image(X2,X7),X1) ) )
| ? [X3,X4,X5] :
( X4 != X5
& X3 = X4
& in(relation_image(X2,X4),X1)
& X3 = X5
& in(relation_image(X2,X5),X1) )
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(ennf_transformation,[],[f39]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ? [X6] :
! [X7] :
( in(X7,X6)
<=> ? [X8] :
( in(X8,powerset(relation_dom(X2)))
& X7 = X8
& in(relation_image(X2,X7),X1) ) )
| ? [X3,X4,X5] :
( X4 != X5
& X3 = X4
& in(relation_image(X2,X4),X1)
& X3 = X5
& in(relation_image(X2,X5),X1) )
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(flattening,[],[f70]) ).
fof(f72,definition,
! [X1,X2] :
( ? [X3,X4,X5] :
( X4 != X5
& X3 = X4
& in(relation_image(X2,X4),X1)
& X3 = X5
& in(relation_image(X2,X5),X1) )
| ~ sP0(X1,X2) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ? [X6] :
! [X7] :
( in(X7,X6)
<=> ? [X8] :
( in(X8,powerset(relation_dom(X2)))
& X7 = X8
& in(relation_image(X2,X7),X1) ) )
| sP0(X1,X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(definition_folding,[],[f71,f72]) ).
fof(f74,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ~ in(X4,powerset(relation_dom(X2)))
| ~ in(relation_image(X2,X4),X1)
| ~ in(X4,X3) )
& ( ( in(X4,powerset(relation_dom(X2)))
& in(relation_image(X2,X4),X1) )
| in(X4,X3) ) )
& element(X1,powerset(powerset(X0)))
& relation(X2)
& function(X2) ),
inference(nnf_transformation,[],[f48]) ).
fof(f75,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ~ in(X4,powerset(relation_dom(X2)))
| ~ in(relation_image(X2,X4),X1)
| ~ in(X4,X3) )
& ( ( in(X4,powerset(relation_dom(X2)))
& in(relation_image(X2,X4),X1) )
| in(X4,X3) ) )
& element(X1,powerset(powerset(X0)))
& relation(X2)
& function(X2) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
( ! [X3] :
( ( ~ in(sK4(X3),powerset(relation_dom(sK3)))
| ~ in(relation_image(sK3,sK4(X3)),sK2)
| ~ in(sK4(X3),X3) )
& ( ( in(sK4(X3),powerset(relation_dom(sK3)))
& in(relation_image(sK3,sK4(X3)),sK2) )
| in(sK4(X3),X3) ) )
& element(sK2,powerset(powerset(sK1)))
& relation(sK3)
& function(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X4,sK4(X3))],[f75]) ).
fof(f93,plain,
! [X1,X2] :
( ? [X3,X4,X5] :
( X4 != X5
& X3 = X4
& in(relation_image(X2,X4),X1)
& X3 = X5
& in(relation_image(X2,X5),X1) )
| ~ sP0(X1,X2) ),
inference(nnf_transformation,[],[f72]) ).
fof(f94,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& in(relation_image(X1,X3),X0)
& X2 = X4
& in(relation_image(X1,X4),X0) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( ( sK22(X0,X1) != sK23(X0,X1)
& sK21(X0,X1) = sK22(X0,X1)
& in(relation_image(X1,sK22(X0,X1)),X0)
& sK21(X0,X1) = sK23(X0,X1)
& in(relation_image(X1,sK23(X0,X1)),X0) )
| ~ sP0(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21,sK22,sK23]),skolemize(X2,sK21(X0,X1)),skolemize(X3,sK22(X0,X1)),skolemize(X4,sK23(X0,X1))],[f94]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ? [X6] :
! [X7] :
( ( in(X7,X6)
| ! [X8] :
( ~ in(X8,powerset(relation_dom(X2)))
| X7 != X8
| ~ in(relation_image(X2,X7),X1) ) )
& ( ? [X8] :
( in(X8,powerset(relation_dom(X2)))
& X7 = X8
& in(relation_image(X2,X7),X1) )
| ~ in(X7,X6) ) )
| sP0(X1,X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(nnf_transformation,[],[f73]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ! [X5] :
( ~ in(X5,powerset(relation_dom(X2)))
| X4 != X5
| ~ in(relation_image(X2,X4),X1) ) )
& ( ? [X6] :
( in(X6,powerset(relation_dom(X2)))
& X4 = X6
& in(relation_image(X2,X4),X1) )
| ~ in(X4,X3) ) )
| sP0(X1,X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(rectify,[],[f96]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ! [X4] :
( ( in(X4,sK24(X1,X2))
| ! [X5] :
( ~ in(X5,powerset(relation_dom(X2)))
| X4 != X5
| ~ in(relation_image(X2,X4),X1) ) )
& ( ( in(sK25(X1,X2,X4),powerset(relation_dom(X2)))
& sK25(X1,X2,X4) = X4
& in(relation_image(X2,X4),X1) )
| ~ in(X4,sK24(X1,X2)) ) )
| sP0(X1,X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24,sK25]),skolemize(X3,sK24(X1,X2)),skolemize(X6,sK25(X1,X2,X4))],[f97]) ).
fof(f99,plain,
function(sK3),
inference(cnf_transformation,[],[f76]) ).
fof(f100,plain,
relation(sK3),
inference(cnf_transformation,[],[f76]) ).
fof(f101,plain,
element(sK2,powerset(powerset(sK1))),
inference(cnf_transformation,[],[f76]) ).
fof(f102,plain,
! [X3] :
( in(relation_image(sK3,sK4(X3)),sK2)
| in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f76]) ).
fof(f103,plain,
! [X3] :
( in(sK4(X3),powerset(relation_dom(sK3)))
| in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f76]) ).
fof(f104,plain,
! [X3] :
( ~ in(relation_image(sK3,sK4(X3)),sK2)
| ~ in(sK4(X3),powerset(relation_dom(sK3)))
| ~ in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f76]) ).
fof(f177,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK21(X0,X1) = sK23(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f179,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK21(X0,X1) = sK22(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f180,plain,
! [X0,X1] :
( sK22(X0,X1) != sK23(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f95]) ).
fof(f181,plain,
! [X2,X0,X1,X4] :
( in(relation_image(X2,X4),X1)
| ~ in(X4,sK24(X1,X2))
| sP0(X1,X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f182,plain,
! [X2,X0,X1,X4] :
( sK25(X1,X2,X4) = X4
| ~ in(X4,sK24(X1,X2))
| sP0(X1,X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f183,plain,
! [X2,X0,X1,X4] :
( in(sK25(X1,X2,X4),powerset(relation_dom(X2)))
| ~ in(X4,sK24(X1,X2))
| sP0(X1,X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f184,plain,
! [X2,X0,X1,X4,X5] :
( in(X4,sK24(X1,X2))
| ~ in(X5,powerset(relation_dom(X2)))
| X4 != X5
| ~ in(relation_image(X2,X4),X1)
| sP0(X1,X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f185,plain,
! [X2,X0,X1,X5] :
( in(X5,sK24(X1,X2))
| ~ in(X5,powerset(relation_dom(X2)))
| ~ in(relation_image(X2,X5),X1)
| sP0(X1,X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(equality_resolution,[],[f184]) ).
fof(f186,plain,
~ element(sK2,powerset(powerset(sK1))),
inference(consistent_polarity_flipping,[],[f101]) ).
fof(f187,plain,
~ function(sK3),
inference(consistent_polarity_flipping,[],[f99]) ).
fof(f240,plain,
! [X2,X0,X1,X5] :
( function(X2)
| ~ in(X5,powerset(relation_dom(X2)))
| ~ in(relation_image(X2,X5),X1)
| sP0(X1,X2)
| element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| in(X5,sK24(X1,X2)) ),
inference(consistent_polarity_flipping,[],[f185]) ).
fof(f241,plain,
! [X2,X0,X1,X4] :
( in(sK25(X1,X2,X4),powerset(relation_dom(X2)))
| ~ in(X4,sK24(X1,X2))
| sP0(X1,X2)
| element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| function(X2) ),
inference(consistent_polarity_flipping,[],[f183]) ).
fof(f242,plain,
! [X2,X0,X1,X4] :
( function(X2)
| ~ in(X4,sK24(X1,X2))
| sP0(X1,X2)
| element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| sK25(X1,X2,X4) = X4 ),
inference(consistent_polarity_flipping,[],[f182]) ).
fof(f243,plain,
! [X2,X0,X1,X4] :
( function(X2)
| ~ in(X4,sK24(X1,X2))
| sP0(X1,X2)
| element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| in(relation_image(X2,X4),X1) ),
inference(consistent_polarity_flipping,[],[f181]) ).
fof(f750,plain,
! [X2,X0,X1] :
( ~ in(X0,sK24(X1,sK3))
| sP0(X1,sK3)
| element(X1,powerset(powerset(X2)))
| ~ relation(sK3)
| in(relation_image(sK3,X0),X1) ),
inference(resolution,[],[f243,f187]) ).
fof(f826,definition,
( spl26_43
<=> relation(sK3) ),
introduced(definition,[new_symbols(definition,[spl26_43])],[avatar_definition]) ).
fof(f828,plain,
( ~ relation(sK3)
| spl26_43 ),
inference(avatar_component_clause,[],[f826]) ).
fof(f830,definition,
( spl26_44
<=> ! [X2,X0,X1] :
( ~ in(X0,sK24(X1,sK3))
| in(relation_image(sK3,X0),X1)
| element(X1,powerset(powerset(X2)))
| sP0(X1,sK3) ) ),
introduced(definition,[new_symbols(definition,[spl26_44])],[avatar_definition]) ).
fof(f831,plain,
( ! [X2,X0,X1] :
( sP0(X1,sK3)
| in(relation_image(sK3,X0),X1)
| element(X1,powerset(powerset(X2)))
| ~ in(X0,sK24(X1,sK3)) )
| ~ spl26_44 ),
inference(avatar_component_clause,[],[f830]) ).
fof(f832,plain,
( ~ spl26_43
| spl26_44 ),
inference(avatar_split_clause,[],[f750,f830,f826]) ).
fof(f1041,plain,
( $false
| spl26_43 ),
inference(resolution,[],[f828,f100]) ).
fof(f1042,plain,
spl26_43,
inference(avatar_contradiction_clause,[],[f1041]) ).
fof(f1043,plain,
( ! [X2,X0,X1] :
( in(relation_image(sK3,X0),X1)
| element(X1,powerset(powerset(X2)))
| ~ in(X0,sK24(X1,sK3))
| sK21(X1,sK3) = sK22(X1,sK3) )
| ~ spl26_44 ),
inference(resolution,[],[f831,f179]) ).
fof(f1045,plain,
( ! [X0,X1] :
( element(sK2,powerset(powerset(X0)))
| ~ in(sK4(X1),sK24(sK2,sK3))
| sK21(sK2,sK3) = sK22(sK2,sK3)
| ~ in(sK4(X1),powerset(relation_dom(sK3)))
| ~ in(sK4(X1),X1) )
| ~ spl26_44 ),
inference(resolution,[],[f1043,f104]) ).
fof(f1052,definition,
( spl26_97
<=> sK21(sK2,sK3) = sK22(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl26_97])],[avatar_definition]) ).
fof(f1056,definition,
( spl26_98
<=> ! [X1] :
( ~ in(sK4(X1),sK24(sK2,sK3))
| ~ in(sK4(X1),X1)
| ~ in(sK4(X1),powerset(relation_dom(sK3))) ) ),
introduced(definition,[new_symbols(definition,[spl26_98])],[avatar_definition]) ).
fof(f1057,plain,
( ! [X1] :
( ~ in(sK4(X1),sK24(sK2,sK3))
| ~ in(sK4(X1),X1)
| ~ in(sK4(X1),powerset(relation_dom(sK3))) )
| ~ spl26_98 ),
inference(avatar_component_clause,[],[f1056]) ).
fof(f1059,definition,
( spl26_99
<=> ! [X0] : element(sK2,powerset(powerset(X0))) ),
introduced(definition,[new_symbols(definition,[spl26_99])],[avatar_definition]) ).
fof(f1060,plain,
( ! [X0] : element(sK2,powerset(powerset(X0)))
| ~ spl26_99 ),
inference(avatar_component_clause,[],[f1059]) ).
fof(f1061,plain,
( spl26_97
| spl26_98
| spl26_99
| ~ spl26_44 ),
inference(avatar_split_clause,[],[f1045,f830,f1059,f1056,f1052]) ).
fof(f1064,definition,
( spl26_100
<=> sP0(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl26_100])],[avatar_definition]) ).
fof(f1065,plain,
( sP0(sK2,sK3)
| ~ spl26_100 ),
inference(avatar_component_clause,[],[f1064]) ).
fof(f1066,plain,
( ~ sP0(sK2,sK3)
| spl26_100 ),
inference(avatar_component_clause,[],[f1064]) ).
fof(f1072,plain,
( ! [X0,X1] :
( in(relation_image(sK3,X0),sK2)
| element(sK2,powerset(powerset(X1)))
| ~ in(X0,sK24(sK2,sK3)) )
| ~ spl26_44
| spl26_100 ),
inference(resolution,[],[f1066,f831]) ).
fof(f1074,definition,
( spl26_102
<=> ! [X0] :
( in(relation_image(sK3,X0),sK2)
| ~ in(X0,sK24(sK2,sK3)) ) ),
introduced(definition,[new_symbols(definition,[spl26_102])],[avatar_definition]) ).
fof(f1075,plain,
( ! [X0] :
( in(relation_image(sK3,X0),sK2)
| ~ in(X0,sK24(sK2,sK3)) )
| ~ spl26_102 ),
inference(avatar_component_clause,[],[f1074]) ).
fof(f1077,plain,
( $false
| ~ spl26_99 ),
inference(resolution,[],[f1060,f186]) ).
fof(f1078,plain,
~ spl26_99,
inference(avatar_contradiction_clause,[],[f1077]) ).
fof(f1079,plain,
( sK21(sK2,sK3) = sK22(sK2,sK3)
| ~ spl26_100 ),
inference(resolution,[],[f1065,f179]) ).
fof(f1080,plain,
( sK21(sK2,sK3) = sK23(sK2,sK3)
| ~ spl26_100 ),
inference(resolution,[],[f1065,f177]) ).
fof(f1081,plain,
( spl26_97
| ~ spl26_100 ),
inference(avatar_split_clause,[],[f1079,f1064,f1052]) ).
fof(f1085,plain,
( sK21(sK2,sK3) != sK22(sK2,sK3)
| ~ sP0(sK2,sK3)
| ~ spl26_100 ),
inference(superposition,[],[f180,f1080]) ).
fof(f1087,plain,
( ~ spl26_100
| ~ spl26_97
| ~ spl26_100 ),
inference(avatar_split_clause,[],[f1085,f1064,f1052,f1064]) ).
fof(f1088,plain,
( spl26_99
| spl26_102
| ~ spl26_44
| spl26_100 ),
inference(avatar_split_clause,[],[f1072,f1064,f830,f1074,f1059]) ).
fof(f1090,plain,
( ! [X0] :
( ~ in(sK4(X0),sK24(sK2,sK3))
| ~ in(sK4(X0),powerset(relation_dom(sK3)))
| ~ in(sK4(X0),X0) )
| ~ spl26_102 ),
inference(resolution,[],[f1075,f104]) ).
fof(f1156,plain,
! [X2,X0,X1] :
( ~ in(X0,sK24(X1,sK3))
| sP0(X1,sK3)
| element(X1,powerset(powerset(X2)))
| ~ relation(sK3)
| sK25(X1,sK3,X0) = X0 ),
inference(resolution,[],[f242,f187]) ).
fof(f1168,definition,
( spl26_108
<=> ! [X2,X0,X1] :
( ~ in(X0,sK24(X1,sK3))
| sK25(X1,sK3,X0) = X0
| element(X1,powerset(powerset(X2)))
| sP0(X1,sK3) ) ),
introduced(definition,[new_symbols(definition,[spl26_108])],[avatar_definition]) ).
fof(f1169,plain,
( ! [X2,X0,X1] :
( sP0(X1,sK3)
| sK25(X1,sK3,X0) = X0
| element(X1,powerset(powerset(X2)))
| ~ in(X0,sK24(X1,sK3)) )
| ~ spl26_108 ),
inference(avatar_component_clause,[],[f1168]) ).
fof(f1170,plain,
( ~ spl26_43
| spl26_108 ),
inference(avatar_split_clause,[],[f1156,f1168,f826]) ).
fof(f1179,plain,
( ~ in(sK4(sK24(sK2,sK3)),sK24(sK2,sK3))
| ~ in(sK4(sK24(sK2,sK3)),powerset(relation_dom(sK3)))
| ~ spl26_98 ),
inference(factoring,[],[f1057]) ).
fof(f1181,definition,
( spl26_110
<=> in(sK4(sK24(sK2,sK3)),powerset(relation_dom(sK3))) ),
introduced(definition,[new_symbols(definition,[spl26_110])],[avatar_definition]) ).
fof(f1183,plain,
( ~ in(sK4(sK24(sK2,sK3)),powerset(relation_dom(sK3)))
| spl26_110 ),
inference(avatar_component_clause,[],[f1181]) ).
fof(f1185,definition,
( spl26_111
<=> in(sK4(sK24(sK2,sK3)),sK24(sK2,sK3)) ),
introduced(definition,[new_symbols(definition,[spl26_111])],[avatar_definition]) ).
fof(f1186,plain,
( in(sK4(sK24(sK2,sK3)),sK24(sK2,sK3))
| ~ spl26_111 ),
inference(avatar_component_clause,[],[f1185]) ).
fof(f1187,plain,
( ~ in(sK4(sK24(sK2,sK3)),sK24(sK2,sK3))
| spl26_111 ),
inference(avatar_component_clause,[],[f1185]) ).
fof(f1189,plain,
( in(sK4(sK24(sK2,sK3)),sK24(sK2,sK3))
| spl26_110 ),
inference(resolution,[],[f1183,f103]) ).
fof(f1190,plain,
( spl26_111
| spl26_110 ),
inference(avatar_split_clause,[],[f1189,f1181,f1185]) ).
fof(f1199,plain,
( ! [X0,X1] :
( sK25(sK2,sK3,X0) = X0
| element(sK2,powerset(powerset(X1)))
| ~ in(X0,sK24(sK2,sK3)) )
| spl26_100
| ~ spl26_108 ),
inference(resolution,[],[f1169,f1066]) ).
fof(f1204,definition,
( spl26_112
<=> ! [X0] :
( sK25(sK2,sK3,X0) = X0
| ~ in(X0,sK24(sK2,sK3)) ) ),
introduced(definition,[new_symbols(definition,[spl26_112])],[avatar_definition]) ).
fof(f1205,plain,
( ! [X0] :
( ~ in(X0,sK24(sK2,sK3))
| sK25(sK2,sK3,X0) = X0 )
| ~ spl26_112 ),
inference(avatar_component_clause,[],[f1204]) ).
fof(f1206,plain,
( spl26_99
| spl26_112
| spl26_100
| ~ spl26_108 ),
inference(avatar_split_clause,[],[f1199,f1168,f1064,f1204,f1059]) ).
fof(f1335,plain,
! [X2,X0,X1] :
( ~ in(X0,powerset(relation_dom(sK3)))
| ~ in(relation_image(sK3,X0),X1)
| sP0(X1,sK3)
| element(X1,powerset(powerset(X2)))
| ~ relation(sK3)
| in(X0,sK24(X1,sK3)) ),
inference(resolution,[],[f240,f187]) ).
fof(f1359,definition,
( spl26_119
<=> ! [X2,X0,X1] :
( ~ in(X0,powerset(relation_dom(sK3)))
| in(X0,sK24(X1,sK3))
| element(X1,powerset(powerset(X2)))
| sP0(X1,sK3)
| ~ in(relation_image(sK3,X0),X1) ) ),
introduced(definition,[new_symbols(definition,[spl26_119])],[avatar_definition]) ).
fof(f1360,plain,
( ! [X2,X0,X1] :
( sP0(X1,sK3)
| in(X0,sK24(X1,sK3))
| element(X1,powerset(powerset(X2)))
| ~ in(X0,powerset(relation_dom(sK3)))
| ~ in(relation_image(sK3,X0),X1) )
| ~ spl26_119 ),
inference(avatar_component_clause,[],[f1359]) ).
fof(f1361,plain,
( ~ spl26_43
| spl26_119 ),
inference(avatar_split_clause,[],[f1335,f1359,f826]) ).
fof(f1364,plain,
( ! [X0,X1] :
( in(X0,sK24(sK2,sK3))
| element(sK2,powerset(powerset(X1)))
| ~ in(X0,powerset(relation_dom(sK3)))
| ~ in(relation_image(sK3,X0),sK2) )
| spl26_100
| ~ spl26_119 ),
inference(resolution,[],[f1360,f1066]) ).
fof(f1375,definition,
( spl26_120
<=> ! [X0] :
( in(X0,sK24(sK2,sK3))
| ~ in(relation_image(sK3,X0),sK2)
| ~ in(X0,powerset(relation_dom(sK3))) ) ),
introduced(definition,[new_symbols(definition,[spl26_120])],[avatar_definition]) ).
fof(f1376,plain,
( ! [X0] :
( ~ in(relation_image(sK3,X0),sK2)
| in(X0,sK24(sK2,sK3))
| ~ in(X0,powerset(relation_dom(sK3))) )
| ~ spl26_120 ),
inference(avatar_component_clause,[],[f1375]) ).
fof(f1377,plain,
( spl26_99
| spl26_120
| spl26_100
| ~ spl26_119 ),
inference(avatar_split_clause,[],[f1364,f1359,f1064,f1375,f1059]) ).
fof(f1378,plain,
( ! [X0] :
( in(sK4(X0),sK24(sK2,sK3))
| ~ in(sK4(X0),powerset(relation_dom(sK3)))
| in(sK4(X0),X0) )
| ~ spl26_120 ),
inference(resolution,[],[f1376,f102]) ).
fof(f1395,plain,
( ~ in(sK4(sK24(sK2,sK3)),powerset(relation_dom(sK3)))
| in(sK4(sK24(sK2,sK3)),sK24(sK2,sK3))
| spl26_111
| ~ spl26_120 ),
inference(resolution,[],[f1378,f1187]) ).
fof(f1414,plain,
( spl26_111
| ~ spl26_110
| spl26_111
| ~ spl26_120 ),
inference(avatar_split_clause,[],[f1395,f1375,f1185,f1181,f1185]) ).
fof(f1415,plain,
( spl26_98
| ~ spl26_102 ),
inference(avatar_split_clause,[],[f1090,f1074,f1056]) ).
fof(f1417,plain,
( ~ spl26_110
| ~ spl26_111
| ~ spl26_98 ),
inference(avatar_split_clause,[],[f1179,f1056,f1185,f1181]) ).
fof(f1423,definition,
( spl26_126
<=> sK4(sK24(sK2,sK3)) = sK25(sK2,sK3,sK4(sK24(sK2,sK3))) ),
introduced(definition,[new_symbols(definition,[spl26_126])],[avatar_definition]) ).
fof(f1425,plain,
( sK4(sK24(sK2,sK3)) = sK25(sK2,sK3,sK4(sK24(sK2,sK3)))
| ~ spl26_126 ),
inference(avatar_component_clause,[],[f1423]) ).
fof(f1428,plain,
( sK4(sK24(sK2,sK3)) = sK25(sK2,sK3,sK4(sK24(sK2,sK3)))
| ~ spl26_111
| ~ spl26_112 ),
inference(resolution,[],[f1186,f1205]) ).
fof(f1437,plain,
( spl26_126
| ~ spl26_111
| ~ spl26_112 ),
inference(avatar_split_clause,[],[f1428,f1204,f1185,f1423]) ).
fof(f1438,plain,
( ! [X0] :
( in(sK4(sK24(sK2,sK3)),powerset(relation_dom(sK3)))
| ~ in(sK4(sK24(sK2,sK3)),sK24(sK2,sK3))
| sP0(sK2,sK3)
| element(sK2,powerset(powerset(X0)))
| ~ relation(sK3)
| function(sK3) )
| ~ spl26_126 ),
inference(superposition,[],[f241,f1425]) ).
fof(f1440,definition,
( spl26_127
<=> function(sK3) ),
introduced(definition,[new_symbols(definition,[spl26_127])],[avatar_definition]) ).
fof(f1442,plain,
( function(sK3)
| ~ spl26_127 ),
inference(avatar_component_clause,[],[f1440]) ).
fof(f1443,plain,
( spl26_127
| ~ spl26_43
| spl26_99
| spl26_100
| ~ spl26_111
| spl26_110
| ~ spl26_126 ),
inference(avatar_split_clause,[],[f1438,f1423,f1181,f1185,f1064,f1059,f826,f1440]) ).
fof(f1444,plain,
( $false
| ~ spl26_127 ),
inference(resolution,[],[f1442,f187]) ).
fof(f1445,plain,
~ spl26_127,
inference(avatar_contradiction_clause,[],[f1444]) ).
cnf(s25,plain,
( ~ spl26_43
| spl26_44 ),
inference(sat_conversion,[],[f832]) ).
cnf(s52,plain,
spl26_43,
inference(sat_conversion,[],[f1042]) ).
cnf(s53,plain,
( ~ spl26_44
| spl26_97
| spl26_98
| spl26_99 ),
inference(sat_conversion,[],[f1061]) ).
cnf(s56,plain,
~ spl26_99,
inference(sat_conversion,[],[f1078]) ).
cnf(s57,plain,
( spl26_97
| ~ spl26_100 ),
inference(sat_conversion,[],[f1081]) ).
cnf(s58,plain,
( ~ spl26_100
| ~ spl26_97
| ~ spl26_100 ),
inference(sat_conversion,[],[f1087]) ).
cnf(s59,plain,
( ~ spl26_97
| ~ spl26_100 ),
inference(rat,[],[s58]) ).
cnf(s60,plain,
( ~ spl26_44
| spl26_99
| spl26_100
| spl26_102 ),
inference(sat_conversion,[],[f1088]) ).
cnf(s63,plain,
( ~ spl26_43
| spl26_108 ),
inference(sat_conversion,[],[f1170]) ).
cnf(s66,plain,
( spl26_110
| spl26_111 ),
inference(sat_conversion,[],[f1190]) ).
cnf(s67,plain,
( spl26_99
| spl26_100
| ~ spl26_108
| spl26_112 ),
inference(sat_conversion,[],[f1206]) ).
cnf(s77,plain,
( ~ spl26_43
| spl26_119 ),
inference(sat_conversion,[],[f1361]) ).
cnf(s78,plain,
( spl26_99
| spl26_100
| ~ spl26_119
| spl26_120 ),
inference(sat_conversion,[],[f1377]) ).
cnf(s82,plain,
( spl26_111
| ~ spl26_110
| spl26_111
| ~ spl26_120 ),
inference(sat_conversion,[],[f1414]) ).
cnf(s83,plain,
( ~ spl26_110
| spl26_111
| ~ spl26_120 ),
inference(rat,[],[s82]) ).
cnf(s84,plain,
( spl26_98
| ~ spl26_102 ),
inference(sat_conversion,[],[f1415]) ).
cnf(s86,plain,
( ~ spl26_98
| ~ spl26_110
| ~ spl26_111 ),
inference(sat_conversion,[],[f1417]) ).
cnf(s89,plain,
( ~ spl26_111
| ~ spl26_112
| spl26_126 ),
inference(sat_conversion,[],[f1437]) ).
cnf(s90,plain,
( ~ spl26_43
| spl26_99
| spl26_100
| spl26_110
| ~ spl26_111
| ~ spl26_126
| spl26_127 ),
inference(sat_conversion,[],[f1443]) ).
cnf(s91,plain,
~ spl26_127,
inference(sat_conversion,[],[f1445]) ).
cnf(s92,plain,
( ~ spl26_43
| spl26_99
| spl26_100
| spl26_110
| ~ spl26_111
| ~ spl26_126 ),
inference(rat,[],[s90,s91]) ).
cnf(s100,plain,
( ~ spl26_44
| spl26_97
| spl26_98 ),
inference(rat,[],[s53,s56]) ).
cnf(s101,plain,
spl26_119,
inference(rat,[],[s77,s52]) ).
cnf(s102,plain,
spl26_108,
inference(rat,[],[s63,s52]) ).
cnf(s103,plain,
spl26_44,
inference(rat,[],[s25,s52]) ).
cnf(s112,plain,
( spl26_110
| spl26_100 ),
inference(rat,[],[s92,s89,s66,s67,s56,s52,s102]) ).
cnf(s113,plain,
spl26_97,
inference(rat,[],[s86,s83,s112,s78,s100,s57,s56,s101,s103]) ).
cnf(s114,plain,
~ spl26_100,
inference(rat,[],[s59,s113]) ).
cnf(s115,plain,
spl26_120,
inference(rat,[],[s78,s101,s56,s114]) ).
cnf(s117,plain,
spl26_102,
inference(rat,[],[s60,s103,s56,s114]) ).
cnf(s118,plain,
spl26_110,
inference(rat,[],[s112,s114]) ).
cnf(s120,plain,
spl26_98,
inference(rat,[],[s84,s117]) ).
cnf(s121,plain,
spl26_111,
inference(rat,[],[s83,s115,s118]) ).
cnf(s122,plain,
$false,
inference(rat,[],[s86,s120,s118,s121]) ).
fof(f1446,plain,
$false,
inference(avatar_sat_refutation,[],[s122]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU297+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n009.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 04:34:45 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.45 % (2661751)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (2661762)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1912336574:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.10/0.45 % (2661757)% WARNING: option uhcvi not known.
% 0.10/0.45 % (2661756)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=952919568_2999 on theBenchmark for (2999ds/0Mi)
% 0.10/0.45 % (2661759)dis+10_1_sil=32000:sp=arity:random_seed=2167701369:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (2661758)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1955050315:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.45 % (2661760)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=836687359:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % (2661761)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2869073273:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.10/0.45 % (2661757)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2994108148:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.10/0.45 % TRYING [1]
% 0.10/0.45 % TRYING [2]
% 0.10/0.45 % TRYING [3]
% 0.10/0.45 % (2661762) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2661751-2661762"...
% 0.10/0.45 % (2661759) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2661751-2661759"...
% 0.10/0.45 % (2661762)...printing done.
% 0.10/0.45 % (2661761) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2661751-2661761"...
% 0.10/0.45 % (2661762)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (2661762)------------------------------
% 0.10/0.45 % (2661762)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (2661762)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (2661762)CaDiCaL version: 2.1.3
% 0.10/0.45 % (2661762)Termination reason: Refutation
% 0.10/0.45 % (2661762)Time elapsed: 0.016 s
% 0.10/0.45 % (2661762)Peak memory usage: 13 MB
% 0.10/0.45 % (2661762)Instructions burned: 42 (million)
% 0.10/0.45 % (2661751)Success in time 0.045 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------